Find the rule for (f ogoh)(x).

Q: Find f(x) if f°(x)=cos x with f(0) =1, f'(0) = 2 , and f'(-)=3.

A: Keep on integrating we are end up with an answer. For those constants we need these initial…

Q: Differentiate the function.      f(x)  =        ______1______                            In x

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Q: Give a characteristic that the two functions f(x)=x and g(x) = 2' have in common.

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Q: Is the function a. EVEN h ODD f(x) 1, -π<x<0 1, 0≤x<T

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Q: Develop a general rule for f(n)(x) given f(x).    f(x) = 1/x

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Q: Differentiate the function. h(x) In x + x² – 7

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Q: Let f(x) = (x + sinx) - 1. Compute f'(x) separately using the Quotient Rule and the Chain Rule. Show…

A: Given f(x)=x+sinx-1

Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: Suppose that f is a function on the interval [1, 3] such that –1 < f(x) < 1 for all x and f(x) dx…

A: It is given that ∫13fxdx=0 and -1≤fx≤1.

Q: Find all a E Z such that f(x) =

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Q: Find the linearization L(x) of the function at f(x) = x4 + 2x2, a = 1 L(x) =

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Q: Find all antiderivatives of function:  f (x) = -4x

A: An antiderivative of a function f(x) is the indefinite integral ∫f(x)dx. Denote this antiderivative…

Q: 1. Use the limit definition of the derivative to find g'(x) if g(x) = 2x² – 6x + 13.

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Q: Find the denhetive f fue function: In(G at

A: Explained below

Q: Use the definitions of increasing and decreasing functions to prove that       f(x) = x3 is…

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Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = e - x 2

A: Consider the given function. fx=e-x2 The function is define for every real value of x. Hence,…

Q: For the function f(x), defined graphically, state the value(s) of x where the function is not…

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Q: Let f be a function defined by f(x) = ln(3 − 2x). What is the maclaurin function expression of the…

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Q: Let f(x)=x²+2x if x<5 - Cx if x 25. For what value of the constant c is the function f continuous on…

A: We have to calculate the value of c

Q: Use the limit formula for the derivative of a function at a point to find f'(-3) for f(r) = 2r2 – r.

A: use limit definition to find the value of derivative.

Q: If x is large, which function grows faster, f(x) g(x) = x2? %3D

A: The given function is fx=2x   and  gx=x2

Q: f(x) = Vx-3

A: Given function is fx=x-3.

Q: Differentiate the following function. f(x) = -3e-3x d -(-3e-³x) = dx

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Q: Consider the function (x)=x²+2x . Using the limit definition of the derivative, show that for any…

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Q: Suppose f'(x) = c for all x, where c is a constant. Show that, for some constant d, f(x) = cx + d.

A: suppose f'(x) =c for all x, where c is constant .Show that for some constant d, f(x)=cx+d

Q: Find f'(1) for f(x) = In(v6x – 3).

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Q: Determine the domain of the function f(x) = In(ln r) + x

A: f(x) = ln(ln x) + x f(x) is not defined if ln x &lt;= 0 [as then ln(ln x) is not defined] ln x &lt;=…

Q: for x 1 x -1 = ( JI- 2 for x = 1, show that flx) is continuous at x = 1

A: If fx=x2-1x-1  for x≠12  for x=1then to show that fx is continuous at x=1.

Q: Suppose f and g are differentiable functions on R such that, (x²+1)f (x) + 3xf(x) = e*2 + 7x and…

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Q: The function f(x)=/25-x' is contionous on

A: It is continuous function.

Q: Show that if f(x) is a non-negative, increasing concavefunction, then ln [ f(x)] is also a concave…

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Q: If the function f(x) = {cos(2πx−a),x&lt;−1x3+1,x≥−1 is continuous, what is the value of a?

A: fx=cos2πx-a,  x&lt;-1        x3+1,    x≥-1 Since Cosine function is continuous for all real numbers,…

Q: Given f(x)=ln(5x), what is f'(x) when x=14.2?

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Q: Find the extrema of the function g(x) = x3 using any of the methods given in the above discussion.

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Q: Differentiate the function. f(x)  = In 1/x

A: Given: The function fx=ln1x, To find: The differentiation of given function.

Q: Find a value of the constant k, if possible, that will make the function continuous everywhere. (kx…

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Q: Find all the x-intercepts of f(x)=cos(x) on the interval [0,2π)

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Q: Assume that we have functions f(x) and g(x) so that

A: Given functions - ∫-13f(x) dx = -1∫35f(x) dx = 4∫-11g(x) dx = 3∫15g(x) dx = 2∫-152f(x)-5g(x)dx = ?

Q: Is the function f(z) = (x2 - y2) + 2xyi entire? Why or why not?

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Q: Develop a general rule for f(n)(x) given f (x).…

A: the function given to us is    f(x) = xn

Q: If a function f is continuous at 0, show that g(x) = xf(x) is differentiable at 0 and find the value…

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Q: Find  f' in terms of g' .

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Q: Show whether the following function is continuously differentiable: f(x,y)=x2y2

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Q: Differentiate the following functions with respect to x using first principle rule. i. f(x) = x²

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: , for x 1 Let f(x) be a function defined by f(x)=- Discuss the contuniuty of f and f'.

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Q: Use the e-d definition to prove that f(x) = x³ + 3 is continuous at xo = 3.

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Q: Use the second derivative to determine f"(3) for the function f(x) = x² In (x) 2ln(3) +2 O 3ln(2) +3…

A: topic - derivatives

Q: For what value of a is the function continuous at every x?

A: